Advanced Statistics: FX System
Advanced Statistics module contributed by Jules Ellis, C2 Member. Jules has written a very helpful guide for these statistics. | |||||
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| ANALYSIS BASED ON MONTHLY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.105 | ||||
| SD | 0.191 | ||||
| Sharpe ratio (Glass type estimate) | -0.550 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.543 | ||||
| df | 56.000 | ||||
| t | -1.199 | ||||
| p | 0.882 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.453 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.357 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.448 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.362 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.608 | ||||
| Upside Potential Ratio | 0.420 | ||||
| Upside part of mean | 0.073 | ||||
| Downside part of mean | -0.178 | ||||
| Upside SD | 0.083 | ||||
| Downside SD | 0.173 | ||||
| N nonnegative terms | 8.000 | ||||
| N negative terms | 49.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 57.000 | ||||
| Mean of predictor | 0.383 | ||||
| Mean of criterion | -0.105 | ||||
| SD of predictor | 0.298 | ||||
| SD of criterion | 0.191 | ||||
| Covariance | -0.002 | ||||
| r | -0.028 | ||||
| b (slope, estimate of beta) | -0.018 | ||||
| a (intercept, estimate of alpha) | -0.098 | ||||
| Mean Square Error | 0.037 | ||||
| DF error | 55.000 | ||||
| t(b) | -0.208 | ||||
| p(b) | 0.582 | ||||
| t(a) | -1.041 | ||||
| p(a) | 0.849 | ||||
| Lowerbound of 95% confidence interval for beta | -0.192 | ||||
| Upperbound of 95% confidence interval for beta | 0.156 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.288 | ||||
| Upperbound of 95% confidence interval for alpha | 0.091 | ||||
| Treynor index (mean / b) | 5.854 | ||||
| Jensen alpha (a) | -0.098 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.127 | ||||
| SD | 0.218 | ||||
| Sharpe ratio (Glass type estimate) | -0.582 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.574 | ||||
| df | 56.000 | ||||
| t | -1.268 | ||||
| p | 0.895 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.485 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.327 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.479 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.332 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.619 | ||||
| Upside Potential Ratio | 0.338 | ||||
| Upside part of mean | 0.069 | ||||
| Downside part of mean | -0.196 | ||||
| Upside SD | 0.078 | ||||
| Downside SD | 0.205 | ||||
| N nonnegative terms | 8.000 | ||||
| N negative terms | 49.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 57.000 | ||||
| Mean of predictor | 0.337 | ||||
| Mean of criterion | -0.127 | ||||
| SD of predictor | 0.278 | ||||
| SD of criterion | 0.218 | ||||
| Covariance | -0.001 | ||||
| r | -0.020 | ||||
| b (slope, estimate of beta) | -0.016 | ||||
| a (intercept, estimate of alpha) | -0.122 | ||||
| Mean Square Error | 0.048 | ||||
| DF error | 55.000 | ||||
| t(b) | -0.147 | ||||
| p(b) | 0.558 | ||||
| t(a) | -1.136 | ||||
| p(a) | 0.870 | ||||
| Lowerbound of 95% confidence interval for beta | -0.227 | ||||
| Upperbound of 95% confidence interval for beta | 0.196 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.336 | ||||
| Upperbound of 95% confidence interval for alpha | 0.093 | ||||
| Treynor index (mean / b) | 8.177 | ||||
| Jensen alpha (a) | -0.122 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.108 | ||||
| Expected Shortfall on VaR | 0.131 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.047 | ||||
| Expected Shortfall on VaR | 0.101 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 57.000 | ||||
| Minimum | 0.667 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.163 | ||||
| Mean of quarter 1 | 0.956 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.027 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 13.000 | ||||
| Percentage of outliers low | 0.228 | ||||
| Mean of outliers low | 0.949 | ||||
| Number of outliers high | 9.000 | ||||
| Percentage of outliers high | 0.158 | ||||
| Mean of outliers high | 1.042 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 1.525 | ||||
| VaR(95%) (moments method) | 0.009 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 1.193 | ||||
| VaR(95%) (regression method) | 0.036 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.075 | ||||
| Quartile 1 | 0.151 | ||||
| Median | 0.227 | ||||
| Quartile 3 | 0.303 | ||||
| Maximum | 0.379 | ||||
| Mean of quarter 1 | 0.075 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.379 | ||||
| Inter Quartile Range | 0.152 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 0.000 | ||||
| Percentage of outliers high | 0.000 | ||||
| Mean of outliers high | NA | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | NA | ||||
| VaR(95%) (moments method) | NA | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | NA | ||||
| VaR(95%) (regression method) | NA | ||||
| Expected Shortfall (regression method) | NA | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | -0.068 | ||||
| Compounded annual return (geometric extrapolation) | -0.079 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.209 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.209 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.608 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.103 | ||||
| SD | 0.215 | ||||
| Sharpe ratio (Glass type estimate) | -0.478 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.477 | ||||
| df | 1253.000 | ||||
| t | -1.045 | ||||
| p | 0.519 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.374 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.418 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.373 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.419 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.656 | ||||
| Upside Potential Ratio | 2.782 | ||||
| Upside part of mean | 0.436 | ||||
| Downside part of mean | -0.539 | ||||
| Upside SD | 0.148 | ||||
| Downside SD | 0.157 | ||||
| N nonnegative terms | 162.000 | ||||
| N negative terms | 1092.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1254.000 | ||||
| Mean of predictor | 0.422 | ||||
| Mean of criterion | -0.103 | ||||
| SD of predictor | 0.340 | ||||
| SD of criterion | 0.215 | ||||
| Covariance | -0.001 | ||||
| r | -0.018 | ||||
| b (slope, estimate of beta) | -0.011 | ||||
| a (intercept, estimate of alpha) | -0.098 | ||||
| Mean Square Error | 0.046 | ||||
| DF error | 1252.000 | ||||
| t(b) | -0.627 | ||||
| p(b) | 0.509 | ||||
| t(a) | -0.994 | ||||
| p(a) | 0.514 | ||||
| Lowerbound of 95% confidence interval for beta | -0.046 | ||||
| Upperbound of 95% confidence interval for beta | 0.024 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.292 | ||||
| Upperbound of 95% confidence interval for alpha | 0.096 | ||||
| Treynor index (mean / b) | 9.172 | ||||
| Jensen alpha (a) | -0.098 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.126 | ||||
| SD | 0.216 | ||||
| Sharpe ratio (Glass type estimate) | -0.583 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.583 | ||||
| df | 1253.000 | ||||
| t | -1.276 | ||||
| p | 0.523 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.480 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.313 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.479 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.313 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.774 | ||||
| Upside Potential Ratio | 2.613 | ||||
| Upside part of mean | 0.426 | ||||
| Downside part of mean | -0.552 | ||||
| Upside SD | 0.142 | ||||
| Downside SD | 0.163 | ||||
| N nonnegative terms | 162.000 | ||||
| N negative terms | 1092.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1254.000 | ||||
| Mean of predictor | 0.365 | ||||
| Mean of criterion | -0.126 | ||||
| SD of predictor | 0.336 | ||||
| SD of criterion | 0.216 | ||||
| Covariance | -0.001 | ||||
| r | -0.014 | ||||
| b (slope, estimate of beta) | -0.009 | ||||
| a (intercept, estimate of alpha) | -0.123 | ||||
| Mean Square Error | 0.047 | ||||
| DF error | 1252.000 | ||||
| t(b) | -0.490 | ||||
| p(b) | 0.507 | ||||
| t(a) | -1.240 | ||||
| p(a) | 0.518 | ||||
| Lowerbound of 95% confidence interval for beta | -0.045 | ||||
| Upperbound of 95% confidence interval for beta | 0.027 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.317 | ||||
| Upperbound of 95% confidence interval for alpha | 0.071 | ||||
| Treynor index (mean / b) | 14.151 | ||||
| Jensen alpha (a) | -0.123 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.022 | ||||
| Expected Shortfall on VaR | 0.028 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.007 | ||||
| Expected Shortfall on VaR | 0.015 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1254.000 | ||||
| Minimum | 0.875 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.139 | ||||
| Mean of quarter 1 | 0.992 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.007 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 203.000 | ||||
| Percentage of outliers low | 0.162 | ||||
| Mean of outliers low | 0.988 | ||||
| Number of outliers high | 167.000 | ||||
| Percentage of outliers high | 0.133 | ||||
| Mean of outliers high | 1.013 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 1.417 | ||||
| VaR(95%) (moments method) | 0.004 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | NA | ||||
| VaR(95%) (regression method) | NA | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 6.000 | ||||
| Minimum | 0.030 | ||||
| Quartile 1 | 0.048 | ||||
| Median | 0.089 | ||||
| Quartile 3 | 0.212 | ||||
| Maximum | 0.463 | ||||
| Mean of quarter 1 | 0.034 | ||||
| Mean of quarter 2 | 0.075 | ||||
| Mean of quarter 3 | 0.103 | ||||
| Mean of quarter 4 | 0.356 | ||||
| Inter Quartile Range | 0.165 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 1.000 | ||||
| Percentage of outliers high | 0.167 | ||||
| Mean of outliers high | 0.463 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | NA | ||||
| VaR(95%) (moments method) | NA | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | NA | ||||
| VaR(95%) (regression method) | NA | ||||
| Expected Shortfall (regression method) | NA | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | -0.068 | ||||
| Compounded annual return (geometric extrapolation) | -0.079 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.170 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.221 | ||||
| Compounded annual return / Expected Shortfall lognormal | -2.853 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.044 | ||||
| SD | 0.000 | ||||
| Sharpe ratio (Glass type estimate) | NA | ||||
| Sharpe ratio (Hedges UMVUE) | NA | ||||
| df | NA | ||||
| t | NA | ||||
| p | NA | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | NA | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | NA | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | NA | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | NA | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -16.186 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -0.044 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 0.003 | ||||
| N nonnegative terms | 0.000 | ||||
| N negative terms | 131.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.066 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.342 | ||||
| SD of criterion | 0.000 | ||||
| Covariance | 0.000 | ||||
| r | NA | ||||
| b (slope, estimate of beta) | NA | ||||
| a (intercept, estimate of alpha) | NA | ||||
| Mean Square Error | NA | ||||
| DF error | NA | ||||
| t(b) | NA | ||||
| p(b) | NA | ||||
| t(a) | NA | ||||
| p(a) | NA | ||||
| Lowerbound of 95% confidence interval for beta | NA | ||||
| Upperbound of 95% confidence interval for beta | NA | ||||
| Lowerbound of 95% confidence interval for alpha | NA | ||||
| Upperbound of 95% confidence interval for alpha | NA | ||||
| Treynor index (mean / b) | NA | ||||
| Jensen alpha (a) | NA | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.044 | ||||
| SD | 0.000 | ||||
| Sharpe ratio (Glass type estimate) | -12492933348697024.000 | ||||
| Sharpe ratio (Hedges UMVUE) | -12420719861132300.000 | ||||
| df | 130.000 | ||||
| t | -8833837887775228.000 | ||||
| p | 1.000 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | NA | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | NA | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -13930479873814932.000 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -10910959848449668.000 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -16.186 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -0.044 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 0.003 | ||||
| N nonnegative terms | 0.000 | ||||
| N negative terms | 131.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.006 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.343 | ||||
| SD of criterion | 0.000 | ||||
| Covariance | 0.000 | ||||
| r | 0.000 | ||||
| b (slope, estimate of beta) | 0.000 | ||||
| a (intercept, estimate of alpha) | -0.044 | ||||
| Mean Square Error | 0.000 | ||||
| DF error | 129.000 | ||||
| t(b) | 0.000 | ||||
| p(b) | 0.500 | ||||
| t(a) | -8658202101255302.000 | ||||
| p(a) | 1.000 | ||||
| Lowerbound of 95% confidence interval for beta | -0.000 | ||||
| Upperbound of 95% confidence interval for beta | 0.000 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.044 | ||||
| Upperbound of 95% confidence interval for alpha | -0.044 | ||||
| Treynor index (mean / b) | -106988867507440387693856969195520.000 | ||||
| Jensen alpha (a) | -0.044 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.000 | ||||
| Expected Shortfall on VaR | 0.000 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.000 | ||||
| Expected Shortfall on VaR | 0.000 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 131.000 | ||||
| Minimum | 1.000 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 1.000 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.000 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 0.000 | ||||
| Percentage of outliers high | 0.000 | ||||
| Mean of outliers high | NA | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | NA | ||||
| VaR(95%) (moments method) | NA | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | NA | ||||
| VaR(95%) (regression method) | NA | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 0.000 | ||||
| Minimum | NA | ||||
| Quartile 1 | NA | ||||
| Median | NA | ||||
| Quartile 3 | NA | ||||
| Maximum | NA | ||||
| Mean of quarter 1 | NA | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | NA | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | NA | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 0.000 | ||||
| Percentage of outliers high | NA | ||||
| Mean of outliers high | NA | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | NA | ||||
| VaR(95%) (moments method) | NA | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | NA | ||||
| VaR(95%) (regression method) | NA | ||||
| Expected Shortfall (regression method) | NA | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.000 | ||||
| Compounded annual return (geometric extrapolation) | 0.000 | ||||
| Calmar ratio (compounded annual return / max draw down) | NA | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.000 | ||||